Explanation:

- Jwala Gutta (Option 3) was the first Indian badminton player to qualify for two events - mixed doubles and women's doubles - in the Olympics. She achieved this feat at the 2012 London Olympics, where she paired with V. Diju in mixed doubles and Ashwini Ponnappa in women’s doubles.

- PV Sindhu (Option 1) is a prominent Indian badminton player known for her achievements in women’s singles, including an Olympic silver and bronze medal, but she has not competed in doubles at the Olympics.

- Saina Nehwal (Option 2) is another top Indian shuttler known for her singles play, having won an Olympic bronze medal, but she has not competed in doubles events at the Olympics.

- Ashwini Ponnappa (Option 4) has competed in women's doubles at the Olympics, but Jwala Gutta was the one who qualified for both doubles events.

Correct Answer: Option 3 - Jwala Gutta